I have a blue point juniper that is growing upward. I plan on training the foliage to stick horizontally, but I want to keep the trunk upward. Would I still need to wire the trunk for support despite not wanting to change its shape?

If the trunk is as you want, there are no reason to wire. Nobody wiers trees in nature and most of them is growing straight.

One reason to wire 'a part of the trunk' is if you are bending/positioning a branch, then you ancor it to a part of the trunk or do two branche principle wireing.